Subgroups — C₂×C₃×C₅×C₃₇₃⋊C₃ #46777071

Order 33570.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₃₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₃₇₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₅×C₃₇₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₃₇₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₃₇₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×C₃₇₃⋊C₃	C₂×C₃	1	3	yes	direct product factor
7	C₂×C₅×C₃₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₃₇₃⋊C₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₃₇₃	C₃×C₅	1	1	yes	characteristic, complemented
10	C₂×C₃₇₃⋊C₃	C₃×C₅	1	3	yes	direct product factor
11	C₅×C₃₇₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₃₇₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
13	C₃₇₃⋊C₃	C₂×C₃×C₅	1	3	yes	direct product factor
14	C₂×C₃₇₃	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₃₇₃	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃²×C₅	—	373	1	no	maximal, Hall
17	C₃²×C₅	—	373	1	no	Hall
18	C₂×C₃×C₅	—	373	3	no	—
19	C₂×C₃×C₅	C₃₇₃⋊C₃	1	1	yes	characteristic, direct product factor
20	C₂×C₃²	—	373	1	no	Hall
21	C₃×C₅	—	373	3	no	—
22	C₃×C₅	C₂×C₃₇₃⋊C₃	1	1	yes	characteristic, direct product factor
23	C₂×C₅	C₃×C₃₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃²	—	373	1	no	Sylow
25	C₂×C₃	—	373	3	no	—
26	C₂×C₃	C₅×C₃₇₃⋊C₃	1	1	yes	characteristic, direct product factor
27	C₅	C₂×C₃×C₃₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₃	—	373	3	no	—
29	C₃	C₂×C₅×C₃₇₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₂	C₃×C₅×C₃₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	C₃₇₃⋊C₃
commutator, cosocle, hypocenter	C₃₇₃	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₃₇₃	C₃
LCS	G ▷ C₃₇₃
UCS	C₁ ◁ C₂×C₃×C₅

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×C₃₇₃⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₃₇₃⋊C₃	C₃	direct (N × H)
3. C₂×C₃×C₅×C₃₇₃	C₃	semidirect
4. C₂×C₃×C₃₇₃⋊C₃	C₅	direct (N × H)
5. C₃×C₅×C₃₇₃	C₂×C₃	semidirect
6. C₅×C₃₇₃⋊C₃	C₂×C₃	direct (N × H)
7. C₂×C₅×C₃₇₃	C₃²	semidirect
8. C₃×C₃₇₃⋊C₃	C₂×C₅	direct (N × H)
9. C₂×C₃×C₃₇₃	C₃×C₅	semidirect
10. C₂×C₃₇₃⋊C₃	C₃×C₅	direct (N × H)
11. C₅×C₃₇₃	C₂×C₃²	semidirect
12. C₃×C₃₇₃	C₂×C₃×C₅	semidirect
13. C₃₇₃⋊C₃	C₂×C₃×C₅	direct (N × H)
14. C₂×C₃₇₃	C₃²×C₅	semidirect
15. C₃₇₃	C₂×C₃²×C₅	semidirect
19. C₂×C₃×C₅	C₃₇₃⋊C₃	direct (N × H)
22. C₃×C₅	C₂×C₃₇₃⋊C₃	direct (N × H)
23. C₂×C₅	C₃×C₃₇₃⋊C₃	direct (N × H)
26. C₂×C₃	C₅×C₃₇₃⋊C₃	direct (N × H)
27. C₅	C₂×C₃×C₃₇₃⋊C₃	direct (N × H)
29. C₃	C₂×C₅×C₃₇₃⋊C₃	direct (N × H)
30. C₂	C₃×C₅×C₃₇₃⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×C₃₇₃⋊C₃	2
C₂×C₅×C₃₇₃⋊C₃	3
C₂×C₃×C₅×C₃₇₃	3
C₂×C₃×C₃₇₃⋊C₃	5
C₂×C₃²×C₅	373

Subgroups — C2×C3×C5×C373⋊C3 #46777071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₃₇₃⋊C₃ #46777071